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arXiv · 1408.6678

Loop Heisenberg-Virasoro Lie Conformal algebra

Guangzhe Fan·Yucai Su·Henan Wu
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Abstract

Let $HV$ be the loop Heisenberg-Virasoro Lie algebra over $\C$ with basis $\{L_{\a,i},H_{\b,j}\,|\,\a,\,\b,i,j\in\Z\}$ and brackets $[L_{\a,i},L_{\b,j}]=(\a-\b)L_{\a+\b,i+j}, [L_{\a,i},H_{\b,j}]=-\b H_{\a+\b,i+j},[H_{\a,i},H_{\b,j}]=0$. In this paper, a formal distribution Lie algebra of $HV$ is constructed. Then the associated conformal algebra $CHV$ is studied, where $CHV$ has a $\C[\partial]$-basis $\{L_i,H_i\,|\,i\in\Z\}$ with $λ$-brackets $[L_i\, {}_λ\, L_j]=(\partial+2λ) L_{i+j}, [L_i\, {}_λ\, H_j]=(\partial+λ) H_{i+j}, [H_i\, {}_λ\, L_j]=λL_{i+j}$ and $[H_i\, {}_λ\, H_j]=0$. In particular, the conformal derivations of $CHV$ are determined. Finally, rank one conformal modules and $\Z$-graded free intermediate series modules over $CHV$ are classified.

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Guangzhe Fan, Yucai Su, Henan Wu. 2014-08-28. Loop Heisenberg-Virasoro Lie Conformal algebra. https://doi.org/10.1063/1.4903990

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